Improved specular point prediction precision using gradient descent algorithm

Global Navigation Satellite Systems Reflectometry (GNSS-R) utilizes GNSS signals reflected off the Earth surface for remote sensing applications. Due to weak power of reflected signals, GNSS-R receiver needs to track reflected signals by open loop. The first step is to calculate the position of specular point. The specular point position error of the existing algorithm—Quasi-Spherical Earth (QSE) Approach—is about 3 km which may cause troubles in data post-processing. In this paper, gradient descent algorithm is applied to calculate position of specular point and the calculation is based on World Geodetic System 1984 (WGS 84) ellipsoid in geodetic coordinate. The benefit of this coordinate is that it is easy to investigate the effect of real surface’s altitude. Learning rate—the key parameter of the algorithm—is adaptively adjusted according to initial error, latitude and gradient descent rate. With self-adaptive learning rate strategy, the algorithm converges fast. Through simulation and test on Global Navigation Satellite System Occultation Sounder II (GNOS II), the performances of the algorithm are validated. The specular point position error of the proposed algorithm is about 10 m. The speed of the proposed algorithm is competitive compared with the existing algorithm. The test on GNOS II shows that the proposed algorithm has good real-time performance.